I did not find a daughter Joanna in the family of John and Lavinia (Brinsmade) Lounsbury. I did find a Joanna b. 1791 among the children of a John and Sarah (Dingee) Lounsbury. Here is the data on the two families:

1. John Lounsbury was born ca 1760. He married Lavinia Brinsmade.
More About John Lounsbury: Parentage not determined
Children of John Lounsbury and Lavinia Brinsmade are:
i. Harmon Lounsbury, b. 1792.
ii. Julian Lounsbury, b. 1794.
iii. Betsey Lounsbury, b. 1796.
iv. Thomas Clark Lounsbury, b. 1789.
v. Elizur Lounsbury, b. 1800.
vi. Mary Maria Lounsbury, b. 1805, probably Bethlehem Twp, Litchfield, CT.

1. John4 Lounsbury (Henry3, John2, Richard1 Lounsberry) was born ca 1755 in Westchester Co., NY, and died 1/1815 in Gagetown, Queens Co., NB. He married Sarah Dingee 1781 in Westchester Co., NY, daughter of Robert Dingee.
Children of John Lounsbury and Sarah Dingee are:
i. Charlotte Ann5 Lounsbury, b. 1781; d. 1860, Sheffield, Sunbury, NB; m. Ebenezer Estabrooks.
ii. Sarah (Sally) Lounsbury, b. ca 1783, NY; d. 1/28/1839; m. Morris Corey, 2/04/1804, Gagetown, Queens Co., NB
iii. Henry Hutchens Lounsbury, b. ca 1787; d. 4/20/1855.
iv. Elizabeth “Betsey” Lounsbury, b. ca 1788.
v. Ann Lounsbury, b. ca 1791.
vi. Joanna Lounsbury, b. 1791; d. 6/10/1865.
vii. Frances Lawton Lounsbury, b. ca 1793; d. Aft. 1814.
viii. John Dingree Lounsbury, b. ca 1795, Gagetown, Queens Co. CA; d. 2/17/1884, Dumfries, York, NB
ix. William Barker Lounsbury, b. 10/31/1797; m. Sarah Corey.
x. Mary Harriet Lounsbury, b. 1801; d. Aft. 1851.